Page 244 - Improving Machinery Reliability

Machiizery Reliability Audits arid Reviews 215

63,000 x 7,000
T= = 98,000 lb-in.
4,500
while its maximum allowable torque value would be

7,,nd3
T=-- - 125,664 ib-in.
16
or about 199 hp/100 rpm. The maximum allowable torque expression in this case
uses zn, = 18,000 psi, the generally accepted "safe allowable" torsional mean stress
for AIS1 4140.
The more conservative approach would be to select a coupling for the higher of
the two torque values. The hub fit-up dimensions would then logically be chosen to
allow slip-free transmission of the higher torque.
Finally, it should be recognized that there is a certain degree of design conservatism
in calculating maximum allowable torque from Equation 3-7 and using 5,000 psi,
10,000 psi, and 11,000 psi as maximum allowable torsional mean stresses for AIS1
1040, 4140, and 4340 steels, respectively. This conservatism may vanish if the com-
bined action of stress concentrations at fillets, superimposed alternating torsional
stresses, or alternating bending stresses from inadequate coupling designs should cause
the combined stresses to go 30% + over the maximum allowable values. In such cases
a Soderberg analysis may be used to more closely establish shaft factors of ~afety.4~3~~

Torsional Holding Ability Can Be Calculated

The torque required to cause complete slippage of a press fit is given by

T = [y p)L d2 (3 - 8)

where p is the coefficient of friction, p the unit press-fit pressure between shaft and
hub, L the length of the hub bore, and d the nominal shaft diameter."7
Using the widely accepted average value of 0.12 for the coefficient of fri~tion?~,~*
Figure 3-89 was plotted to show the relationship between torsional holding ability
(or requirement), press-fit pressures, and coupling-bore dimensions. The press-fit
pressures refer to ratios of shaft diameter over hub diameter d/D, and interference
fits. Figure 3-90 illustrates this relationship which is based on the mathematical
expression for press-fit contact pressures of steel hubs on solid steel shafts:

In this formula, e represents the total diametral interference and E is the modulus of
elasticity for Alternatively, contact pressure could be expressed as a function
of the interference rate i. This rate equals the diametral interference divided by the
shaft diameter; e.g., in./in. or mdmm: